Why is it not possible to experience an authentic French sauce by frying mushroom in Crème Fraîche?

Before put the crème fraîche, fry your mushrooms in some oil and butter ( more or less 50 / 50), once they are golden add the crème + salt and pepper..

I'm French by the way.

If you saute some mushrooms in a little seasoned butter, then add some crème fraiche, you'll have a creamy mushroom sauce, not sure about the authenticity though.

The French mushroom sauce is called Sauce Morel. It is a beefy sauce with heavy cream added. If you're not just trolling, the source below is a video of a French chef making sauce morel.

The French use special ingredients like basil pesto.

Maybe they don't make mushroom sauce that way in France. If they don't, then a mushroom sauce made that way can't be authentically French.

Since that is a white, um, sauce, why would you fry mushrooms in it, knowing well that mushrooms will give up their water and possibly dilute the sauce?